Solve for $x$ and $y$ using elimination. ${x+3y = 38}$ ${-x+5y = 42}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $8y = 80$ $\dfrac{8y}{{8}} = \dfrac{80}{{8}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {x+3y = 38}\thinspace$ to find $x$ ${x + 3}{(10)}{= 38}$ $x+30 = 38$ $x+30{-30} = 38{-30}$ ${x = 8}$ You can also plug ${y = 10}$ into $\thinspace {-x+5y = 42}\thinspace$ and get the same answer for $x$ : ${-x + 5}{(10)}{= 42}$ ${x = 8}$